Monthly Archives: June 2009

Here’s a picture to announce a summer posting pause. We’re working hard on brilliant new features, for a relaunch in a few weeks. But meanwhile explore the archive – there’s stacks on the site now, and it’s almost all new stuff, not the versions you see on lots of illusion sites. Try putting the name of any illusion that interests you into the search box at the bottom of the lists to the right. Or explore popular categories, like Impossible Worlds. And don’t forget (if you’ve been here before) that there are now nearly a hundred brilliant mini illusions for you to download for your own sites.

This picture is a Photoshop fantasy rather an illusion, but it’s here because I like bubbles. I think the creature is a gecko, (please comment if I got that wrong). The background and sky is from the Nile in Egypt, but I snapped the gecko in the London Zoo. There’s an earlier post on how I photograph the bubbles. For all the bubble picture posts (and some nice ice) see the category Soap Bubble Pictures.

Just about our first post was a tessellation tutorial. It was quite comprehensive, but a bit heavy going. I’ve been wanting to post an animated demo, because I reckon that seeing that first would make the tutorial much easier to follow. So the animation is below, but first, a reminder of the basics:

A tessellation is a pattern like the one above. The cells of the pattern fit together like jig-saw pieces, with no gaps and no overlaps. You can’t make a pattern like that out of just any old shape. It only works with shapes whose edges can be snipped into pairs of segments with special properties. The two segments in each pair must be indentical, except that they may be either reflections of one another, or rotated in relation to one another, like the hands of an old-fashioned clock. Confused already? Just watch this animation, showing the evolution of the pattern above, and you’ll see how it all works.

If you can see this illusion, you may be amazed to discover it’s not an animation. Most people will see waving movement, yet the pattern of lozenges is not really moving at all. But about 5% of people just don’t see this kind of illusion, and if that’s you, it doesn’t mean anything’s wrong. If you do see the movement, it won’t be wherever in the pattern you focus, but in the periphery of your field of view. However, the effect is also very sensitive to size. I see it vividly with the screen about 15 inches (36 cms) from my eyes, and the image 8 inches (21.5 cms) wide on the screen, but I think you’ll get an even better effect by clicking on the image, if a bigger version then comes up on your system.

It’s a kind of illusion only discovered in the last few years. Lots of discoveries about it have been made by Japanese researcher Akiyoshi Kitaoka, and on his site (amongst scores of other stunning illusions) you’ll find his masterpiece in this line, his famous rotating snakes illusion. Update 4/9/12! I just found out that the image I based this picture on is also one of Kitaoka’s. I just changed it to make the pattern more wavy.

Upper left is the classic Poggendorff figure: the oblique lines are objectively aligned, but the upper one appears shifted just a bit to the left. There are lots of variants on this illusion. For example, about forty years ago, researcher Stanley Coren showed that the effect persists, weakly, when the configuration is reduced to dots, as at upper middle. And top right is another variant, the Poggendorff-Without-Parallels: the misalignment effect persists, weakly, in two objectively aligned segments even without the long parallel inducing lines. Most researchers have found that this last effect is greatest when the test arms are at an angle of around 22 degrees from vertical. An analogous affect shows up when they are rotated the same amount form horizontal.

To my eye, the Poggendorff-Without-Parallels effect even appears when the little test line segments are reduced just to dots, as shown lower left. Imagine joining up each of the three pairs of dots with the isolated dot, so that we end up with three triangles. If we then drop a vertical line from the isolated dot to the middle pair of dots, it will pass through the mid-point in between them, as diagrammed in yellow to the right. So the middle triangle of dots has sides of equal length, or is equilateral, as the geometers call it, and that’s just how it looks. No surprises so far. But now here’s the interesting bit. The two other triangles of dots, rotated respectively clockwise and anti-clockwise from vertical, remain objectively equilateral, but that’s not how I see them. For me they now look more like right-angles triangles, as diagrammed with yellow lines to the right. The effect suggests a shift in apparent position of the right hand pair of dots, (rotated anti-clockwise about 22 degrees from vertical), just about equivalent to the shift we seem to see in the Poggendorff-Without-Parallels, shown above it at top right. There’s an equivalent shift for me in the pair of dots rotated around 22 degrees from horizontal.

It would be really useful to have comments on whether that works for you, or whether for you the rotated dot arrays still present equilateral triangle arrangements. Illusions like these often do look different to different observers, and it’s also all to easy, once you have a theory about what’s going on, to see things the way your theory says they should look.

11 June 2012: This is a revision of the original post. It included a 3D demo of the dotty effect, but with triangles of dots that turned out not to be truly equilateral…. Woops.